Question

If alpha and beta arethe zeros of the quadratic polynomial f(x)=x^2-x-4,find the value of 1/alpha+1/beta-1/alpha beta

Answer 1

$\huge {\textbf {\underline {\underline {ANSWER}}}}$

f ( x ) = x^2 - x - 4

Here a = 1 b = - 1 c = - 4

$if \: \: \alpha \: and \: \beta \: are \: roots \: of \: f(x) \\ \\ \\ \alpha + \beta = \frac{ - ( - 1)}{1} \\ \\ \\ = 1 \\ \\ \\ \alpha \beta = \frac{ - 4}{1} \\ \\ \\ = - 4 \\ \\ \\ \frac{1}{ \alpha } + \frac{1}{ \beta } - \frac{1}{ \alpha \beta } \\ \\ \\ = \frac{ \alpha + \beta }{ \alpha \beta } - \frac{1}{ \alpha \beta } \\ \\ \\ = \frac{1}{4} - \frac{1}{4} \\ \\ \\ = 0$